It's Good For You
Karl packed up and headed out for a month long vacation.Before leaving,he gave a spare key to Zaux and asked him to housesit while he was gone.The next day,Zaux went over to Karl's house,took in the mail,feed the fish then decided to have a look around.When he made his way down to the basement,his face lit up with a smile from ear to ear.Turns out Karl made all kinds of juices which he kept in large tanks lining the walls.
Zaux found the tank labelled "Carrot Juice-Grade A" and saw it contained 100 litres.He thought if he were to help himself to a litre of the juice and then replace it with a litre of water,Karl would be none the wiser.And so that's what he did,thinking it would be just this one time.However,on the second day,Zaux couldn't stop himself from doing the same thing.He took out a litre of juice and replaced it with a litre of water.Needless to say,Zaux repeated this process once a day,ever day till Karl returned home 30 days later.
All in all,Zaux removed 30 litres from the tank (1 litre of juice and 29 litres of juice/water mixture).
How much carrot juice did Karl lose?
Zaux found the tank labelled "Carrot Juice-Grade A" and saw it contained 100 litres.He thought if he were to help himself to a litre of the juice and then replace it with a litre of water,Karl would be none the wiser.And so that's what he did,thinking it would be just this one time.However,on the second day,Zaux couldn't stop himself from doing the same thing.He took out a litre of juice and replaced it with a litre of water.Needless to say,Zaux repeated this process once a day,ever day till Karl returned home 30 days later.
All in all,Zaux removed 30 litres from the tank (1 litre of juice and 29 litres of juice/water mixture).
How much carrot juice did Karl lose?
posted by Knightmare at
3:48 PM
11 Comments:
Karl lost almost 26.03 litres of carrot juice. I can't imagine Zaux wanting stale carrot juice.
aaaagggggggggggggg!
didn`t think it would be answered so fast!
Chris-for full points,show your work
You asked for it, so i'll oblige. Let V be the initial amount of carrot
juice. Let v be the volume exchanged. Let V[n] be the amount of
carrot juice remaining in the container after the n th sampling and
water enhancement. Then after the n+1 th tasting there wll be:
V[n+1] = V[n] - v*V[n]/V left => V[n+1] = V[n](1 - v/V). Using that
recursion formula along with with V[0] = V => V[1] = V(1 - v/V),
V[2] = V[1](1 - v/V) = V(1 - v/V)² => V[n] = V(1 - v/V)ⁿ.
Using V = 100, v = 1 and n = 30 => 100 * 0.99^30 ≈ 73.97 litres.
So approx 26.03 litres was unstintingly tested by Zaux for Karl.
Sorry I got it too quickly. In consolation, I made a dog's dinner of it before coming up with the reasoning.
Really a kick post. After 100 exchanges, there would be ≈ 36.6 l left.
I must have mentioned it, or it's a weird coincidence ... but I actually juice 3 times a day ... carrot and apple juice is my favorite ...:)
full points awarded
100*0.99^n----that's exactly what the source said---you got her
Zaux, surely you don't believe in coincidence, I think it scientifically proves that Knightmare is telepathic and that Pequod is an alien spaceship ;)
Chris...how did you know that i am telepathic?
btw:the answer to your next posted question is 1728.
I know.
Nice back and forth guys, enjoyed it.
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